Excluding foreclosures and short sales, which sell at deep discounts to the market price, home prices were up 7.5% on a year-on-year basis and 0.9% month-on-month.

The states with the highest home-price appreciation in December were Arizona (20%), Nevada (15.3%), Idaho (14.6%), California (12.6%) and Hawaii (12.5%).

"We are heading into 2013 with home prices on the rebound," said Anand Nallathambi, president and CEO of CoreLogic. "All signals point to a continued improvement in the fundamentals underpinning the U.S. housing market recovery."

Housing appears to have some momentum, with prices expected to rise 7.9% in January from a year earlier, according to Core Logic's Pending Home Sales Index. Month over month, prices are likely to decline by 1%, reflecting the seasonal winter slowdown.

Excluding foreclosures and short sales, which sell at deep discounts to market prices, home prices are likely to rise 8.6% on a year-on-year basis and 0.7% on a month-on-month basis in January.